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Vertex configuration

Index Vertex configuration

In geometry, a vertex configuration by Walter Steurer, Sofia Deloudi, (2009) pp. [1]

179 relations: Alternated octagonal tiling, Alternated order-4 hexagonal tiling, Angular defect, Antiprism, Apeirogonal antiprism, Apeirogonal hosohedron, Apeirogonal prism, Archimedean solid, Bipyramid, Branko Grünbaum, Cantic octagonal tiling, Catalan solid, Chirality (mathematics), Cube, Cuboctahedron, Dodecahedron, Elongated triangular tiling, Face (geometry), Geoffrey Colin Shephard, Geometry, Great dodecahedron, Great icosahedron, Great pentagonal hexecontahedron, Great pentagrammic hexecontahedron, Great retrosnub icosidodecahedron, Great snub icosidodecahedron, Great stellated dodecahedron, Heptagonal tiling, Hexagonal tiling, Hexaoctagonal tiling, Hosohedron, Icosahedron, Icosidodecahedron, Infinite-order apeirogonal tiling, Infinite-order pentagonal tiling, Infinite-order square tiling, Infinite-order triangular tiling, Isogonal figure, Isohedral figure, Martyn Cundy, Octagonal tiling, Octahedron, Order-3 apeirogonal tiling, Order-4 apeirogonal tiling, Order-4 heptagonal tiling, Order-4 hexagonal tiling, Order-4 octagonal tiling, Order-4 pentagonal tiling, Order-5 apeirogonal tiling, Order-5 hexagonal tiling, ..., Order-5 pentagonal tiling, Order-5 square tiling, Order-6 hexagonal tiling, Order-6 octagonal tiling, Order-6 pentagonal tiling, Order-6 square tiling, Order-7 heptagonal tiling, Order-7 square tiling, Order-7 triangular tiling, Order-8 hexagonal tiling, Order-8 octagonal tiling, Order-8 square tiling, Order-8 triangular tiling, Orthographic projection, Pentaapeirogonal tiling, Pentagon, Pentagram, Pentahexagonal tiling, Platonic solid, Polygon, Prism (geometry), Quarter order-6 square tiling, Rhombic dodecahedron, Rhombicosidodecahedron, Rhombicuboctahedron, Rhombihexaoctagonal tiling, Rhombipentahexagonal tiling, Rhombitetraapeirogonal tiling, Rhombitetraheptagonal tiling, Rhombitetrahexagonal tiling, Rhombitetraoctagonal tiling, Rhombitetrapentagonal tiling, Rhombitriapeirogonal tiling, Rhombitriheptagonal tiling, Rhombitrihexagonal tiling, Rhombitrioctagonal tiling, Rhombus, Schläfli symbol, Semiregular polyhedron, Small hexagrammic hexecontahedron, Small retrosnub icosicosidodecahedron, Small stellated dodecahedron, Snub apeiroapeirogonal tiling, Snub cube, Snub dodecahedron, Snub heptaheptagonal tiling, Snub hexahexagonal tiling, Snub hexaoctagonal tiling, Snub octaoctagonal tiling, Snub order-6 square tiling, Snub order-8 triangular tiling, Snub pentahexagonal tiling, Snub pentapentagonal tiling, Snub square tiling, Snub tetraapeirogonal tiling, Snub tetraheptagonal tiling, Snub tetrahexagonal tiling, Snub tetraoctagonal tiling, Snub tetrapentagonal tiling, Snub triapeirogonal tiling, Snub triheptagonal tiling, Snub trihexagonal tiling, Snub trioctagonal tiling, Spherical polyhedron, Square tiling, Star polygon, Stella (software), Tetraapeirogonal tiling, Tetrahedron, Tetraheptagonal tiling, Tetrahexagonal tiling, Tetraoctagonal tiling, Tetrapentagonal tiling, Trapezohedron, Triangle, Triangular tiling, Triapeirogonal tiling, Triheptagonal tiling, Trihexagonal tiling, Trioctagonal tiling, Truncated cube, Truncated cuboctahedron, Truncated dodecahedron, Truncated heptagonal tiling, Truncated hexagonal tiling, Truncated hexaoctagonal tiling, Truncated icosahedron, Truncated icosidodecahedron, Truncated infinite-order square tiling, Truncated infinite-order triangular tiling, Truncated octagonal tiling, Truncated octahedron, Truncated order-3 apeirogonal tiling, Truncated order-4 apeirogonal tiling, Truncated order-4 heptagonal tiling, Truncated order-4 hexagonal tiling, Truncated order-4 octagonal tiling, Truncated order-4 pentagonal tiling, Truncated order-5 hexagonal tiling, Truncated order-5 pentagonal tiling, Truncated order-5 square tiling, Truncated order-6 hexagonal tiling, Truncated order-6 octagonal tiling, Truncated order-6 pentagonal tiling, Truncated order-6 square tiling, Truncated order-7 heptagonal tiling, Truncated order-7 square tiling, Truncated order-7 triangular tiling, Truncated order-8 hexagonal tiling, Truncated order-8 octagonal tiling, Truncated order-8 triangular tiling, Truncated pentahexagonal tiling, Truncated square tiling, Truncated tetraapeirogonal tiling, Truncated tetrahedron, Truncated tetraheptagonal tiling, Truncated tetrahexagonal tiling, Truncated tetraoctagonal tiling, Truncated tetrapentagonal tiling, Truncated triapeirogonal tiling, Truncated triheptagonal tiling, Truncated trihexagonal tiling, Truncated trioctagonal tiling, Uniform polyhedron, Uniform tilings in hyperbolic plane, Vertex (geometry), Vertex figure, 3-7 kisrhombille, 4-5 kisrhombille. Expand index (129 more) »

Alternated octagonal tiling

In geometry, the tritetragonal tiling or alternated octagonal tiling is a uniform tiling of the hyperbolic plane.

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Alternated order-4 hexagonal tiling

In geometry, the alternated order-4 hexagonal tiling or ditetragonal tritetratrigonal tiling is a uniform tiling of the hyperbolic plane.

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Angular defect

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would.

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Antiprism

In geometry, an n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles.

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Apeirogonal antiprism

In geometry, an apeirogonal antiprism or infinite antiprism is the arithmetic limit of the family of antiprisms; it can be considered an infinite polyhedron or a tiling of the plane.

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Apeirogonal hosohedron

In geometry, an apeirogonal hosohedron or infinite hosohedron is a tiling of the plane consisting of two vertices at infinity.

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Apeirogonal prism

In geometry, an apeirogonal prism or infinite prism is the arithmetic limit of the family of prisms; it can be considered an infinite polyhedron or a tiling of the plane.

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Archimedean solid

In geometry, an Archimedean solid is one of the 13 solids first enumerated by Archimedes.

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Bipyramid

An n-gonal bipyramid or dipyramid is a polyhedron formed by joining an n-gonal pyramid and its mirror image base-to-base.

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Branko Grünbaum

Branko Grünbaum (ברנקו גרונבאום; born 2 October 1929) is a Yugoslavian-born mathematician and a professor emeritus at the University of Washington in Seattle.

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Cantic octagonal tiling

In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane.

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Catalan solid

In mathematics, a Catalan solid, or Archimedean dual, is a dual polyhedron to an Archimedean solid.

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Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Cuboctahedron

In geometry, a cuboctahedron is a polyhedron with 8 triangular faces and 6 square faces.

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Elongated triangular tiling

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Geoffrey Colin Shephard

Geoffrey Colin Shephard is a mathematician who works on convex geometry and reflection groups.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Great dodecahedron

In geometry, the great dodecahedron is a Kepler–Poinsot polyhedron, with Schläfli symbol and Coxeter–Dynkin diagram of.

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Great icosahedron

In geometry, the great icosahedron is one of four Kepler-Poinsot polyhedra (nonconvex regular polyhedra), with Schläfli symbol and Coxeter-Dynkin diagram of.

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Great pentagonal hexecontahedron

In geometry, the great pentagonal hexecontahedron is a nonconvex isohedral polyhedron.

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Great pentagrammic hexecontahedron

In geometry, the great pentagrammic hexecontahedron is a nonconvex isohedral polyhedron.

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Great retrosnub icosidodecahedron

In geometry, the great retrosnub icosidodecahedron or great inverted retrosnub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U74.

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Great snub icosidodecahedron

In geometry, the great snub icosidodecahedron is a nonconvex uniform polyhedron, indexed as U57.

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Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

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Heptagonal tiling

In geometry, the heptagonal tiling is a regular tiling of the hyperbolic plane.

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Hexagonal tiling

In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which three hexagons meet at each vertex.

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Hexaoctagonal tiling

In geometry, the hexaoctagonal tiling is a uniform tiling of the hyperbolic plane.

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Hosohedron

In geometry, an ''n''-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Icosidodecahedron

In geometry, an icosidodecahedron is a polyhedron with twenty (icosi) triangular faces and twelve (dodeca) pentagonal faces.

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Infinite-order apeirogonal tiling

In geometry, the infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane.

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Infinite-order pentagonal tiling

In 2-dimensional hyperbolic geometry, the infinite-order pentagonal tiling is a regular tiling.

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Infinite-order square tiling

In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane.

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Infinite-order triangular tiling

In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

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Isogonal figure

In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure.

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Isohedral figure

In geometry, a polytope of dimension 3 (a polyhedron) or higher is isohedral or face-transitive when all its faces are the same.

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Martyn Cundy

Henry Martyn Cundy (23 December 1913 – 25 February 2005) was a mathematics teacher and professor in Britain and Malawi as well as a singer, musician and poet.

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Octagonal tiling

In geometry, the octagonal tiling is a regular tiling of the hyperbolic plane.

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Order-3 apeirogonal tiling

In geometry, the order-3 apeirogonal tiling is a regular tiling of the hyperbolic plane.

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Order-4 apeirogonal tiling

In geometry, the order-4 apeirogonal tiling is a regular tiling of the hyperbolic plane.

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Order-4 heptagonal tiling

In geometry, the order-4 heptagonal tiling is a regular tiling of the hyperbolic plane.

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Order-4 hexagonal tiling

In geometry, the order-4 hexagonal tiling is a regular tiling of the hyperbolic plane.

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Order-4 octagonal tiling

In geometry, the order-4 octagonal tiling is a regular tiling of the hyperbolic plane.

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Order-4 pentagonal tiling

In geometry, the order-4 pentagonal tiling is a regular tiling of the hyperbolic plane.

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Order-5 apeirogonal tiling

In geometry, the order-5 apeirogonal tiling is a regular tiling of the hyperbolic plane.

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Order-5 hexagonal tiling

In geometry, the order-5 hexagonal tiling is a regular tiling of the hyperbolic plane.

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Order-5 pentagonal tiling

In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane.

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Order-5 square tiling

In geometry, the order-5 square tiling is a regular tiling of the hyperbolic plane.

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Order-6 hexagonal tiling

In geometry, the order-6 hexagonal tiling is a regular tiling of the hyperbolic plane.

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Order-6 octagonal tiling

In geometry, the order-6 octagonal tiling is a regular tiling of the hyperbolic plane.

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Order-6 pentagonal tiling

In geometry, the order-6 pentagonal tiling is a regular tiling of the hyperbolic plane.

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Order-6 square tiling

In geometry, the order-6 square tiling is a regular tiling of the hyperbolic plane.

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Order-7 heptagonal tiling

In geometry, the order-7 heptagonal tiling is a regular tiling of the hyperbolic plane.

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Order-7 square tiling

In geometry, the order-7 square tiling is a regular tiling of the hyperbolic plane.

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Order-7 triangular tiling

In geometry, the order-7 triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of.

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Order-8 hexagonal tiling

In geometry, the order-8 hexagonal tiling is a regular tiling of the hyperbolic plane.

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Order-8 octagonal tiling

In geometry, the order-8 octagonal tiling is a regular tiling of the hyperbolic plane.

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Order-8 square tiling

In geometry, the order-8 square tiling is a regular tiling of the hyperbolic plane.

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Order-8 triangular tiling

In geometry, the order-8 triangular tiling is a regular tiling of the hyperbolic plane.

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Orthographic projection

Orthographic projection (sometimes orthogonal projection), is a means of representing three-dimensional objects in two dimensions.

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Pentaapeirogonal tiling

In geometry, the pentaapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Pentagram

A pentagram (sometimes known as a pentalpha or pentangle or a star pentagon) is the shape of a five-pointed star drawn with five straight strokes.

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Pentahexagonal tiling

In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

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Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

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Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

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Quarter order-6 square tiling

In geometry, the quarter order-6 square tiling is a uniform tiling of the hyperbolic plane.

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Rhombic dodecahedron

In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces.

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Rhombicosidodecahedron

In geometry, the rhombicosidodecahedron, or small rhombicosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces.

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Rhombicuboctahedron

In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces.

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Rhombihexaoctagonal tiling

In geometry, the rhombihexaoctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Rhombipentahexagonal tiling

In geometry, the rhombipentahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitetraapeirogonal tiling

In geometry, the rhombitetraapeirogonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitetraheptagonal tiling

In geometry, the rhombitetraheptagonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitetrahexagonal tiling

In geometry, the rhombitetrahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitetraoctagonal tiling

In geometry, the rhombitetraoctagonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitetrapentagonal tiling

In geometry, the rhombitetrapentagonal tiling is a uniform tiling of the hyperbolic plane.

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Rhombitriapeirogonal tiling

In geometry, the rhombtriapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of rr.

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Rhombitriheptagonal tiling

In geometry, the rhombitriheptagonal tiling is a semiregular tiling of the hyperbolic plane.

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Rhombitrihexagonal tiling

In geometry, the rhombitrihexagonal tiling is a semiregular tiling of the Euclidean plane.

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Rhombitrioctagonal tiling

In geometry, the rhombitrioctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Rhombus

In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.

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Schläfli symbol

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

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Semiregular polyhedron

The term semiregular polyhedron (or semiregular polytope) is used variously by different authors.

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Small hexagrammic hexecontahedron

In geometry, the small hexagrammic hexecontahedron is a nonconvex isohedral polyhedron.

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Small retrosnub icosicosidodecahedron

In geometry, the small retrosnub icosicosidodecahedron or small inverted retrosnub icosicosidodecahedron is a nonconvex uniform polyhedron, indexed as U72.

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Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

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Snub apeiroapeirogonal tiling

In geometry, the snub apeiroapeirogonal tiling is a uniform tiling of the hyperbolic plane.

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Snub cube

In geometry, the snub cube, or snub cuboctahedron, is an Archimedean solid with 38 faces: 6 squares and 32 equilateral triangles.

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Snub dodecahedron

In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

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Snub heptaheptagonal tiling

In geometry, the snub heptaheptagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub hexahexagonal tiling

In geometry, the snub hexahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub hexaoctagonal tiling

In geometry, the snub hexaoctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Snub octaoctagonal tiling

In geometry, the snub octaoctagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub order-6 square tiling

In geometry, the snub tetratritetragonal tiling or snub order-6 square tiling is a uniform tiling of the hyperbolic plane.

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Snub order-8 triangular tiling

In geometry, the snub tritetratrigonal tiling or snub order-8 triangular tiling is a uniform tiling of the hyperbolic plane.

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Snub pentahexagonal tiling

In geometry, the snub pentahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub pentapentagonal tiling

In geometry, the snub pentapentagonal tiling is a regular tiling of the hyperbolic plane.

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Snub square tiling

In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane.

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Snub tetraapeirogonal tiling

In geometry, the snub tetrapeirogonal tiling is a uniform tiling of the hyperbolic plane.

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Snub tetraheptagonal tiling

In geometry, the snub tetraheptagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub tetrahexagonal tiling

In geometry, the snub tetrahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub tetraoctagonal tiling

In geometry, the snub tetraoctagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub tetrapentagonal tiling

In geometry, the snub tetrapentagonal tiling is a uniform tiling of the hyperbolic plane.

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Snub triapeirogonal tiling

In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr.

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Snub triheptagonal tiling

In geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane.

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Snub trihexagonal tiling

In geometry, the snub hexagonal tiling (or snub trihexagonal tiling) is a semiregular tiling of the Euclidean plane.

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Snub trioctagonal tiling

In geometry, the order-3 snub octagonal tiling is a semiregular tiling of the hyperbolic plane.

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Spherical polyhedron

In mathematics, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons.

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Square tiling

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane.

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Star polygon

In geometry, a star polygon is a type of non-convex polygon.

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Stella (software)

Stella, a computer program available in three versions (Great Stella, Small Stella and Stella4D), was created by Robert Webb of Australia.

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Tetraapeirogonal tiling

In geometry, the tetraapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Tetraheptagonal tiling

In geometry, the tetraheptagonal tiling is a uniform tiling of the hyperbolic plane.

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Tetrahexagonal tiling

In geometry, the tetrahexagonal tiling is a uniform tiling of the hyperbolic plane.

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Tetraoctagonal tiling

In geometry, the tetraoctagonal tiling is a uniform tiling of the hyperbolic plane.

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Tetrapentagonal tiling

In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane.

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Trapezohedron

The n-gonal trapezohedron, antidipyramid, antibipyramid or deltohedron is the dual polyhedron of an n-gonal antiprism.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Triangular tiling

In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane.

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Triapeirogonal tiling

In geometry, the triapeirogonal tiling (or trigonal-horocyclic tiling) is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r.

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Triheptagonal tiling

In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling.

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Trihexagonal tiling

In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons.

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Trioctagonal tiling

In geometry, the trioctagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 octagonal tiling.

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Truncated cube

In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid.

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Truncated cuboctahedron

In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.

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Truncated dodecahedron

In geometry, the truncated dodecahedron is an Archimedean solid.

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Truncated heptagonal tiling

In geometry, the truncated heptagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated hexagonal tiling

In geometry, the truncated hexagonal tiling is a semiregular tiling of the Euclidean plane.

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Truncated hexaoctagonal tiling

In geometry, the truncated hexaoctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated icosahedron

In geometry, the truncated icosahedron is an Archimedean solid, one of 13 convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.

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Truncated icosidodecahedron

In geometry, the truncated icosidodecahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.

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Truncated infinite-order square tiling

In geometry, the truncated infinite-order square tiling is a uniform tiling of the hyperbolic plane.

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Truncated infinite-order triangular tiling

In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t.

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Truncated octagonal tiling

In geometry, the Truncated octagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated octahedron

In geometry, the truncated octahedron is an Archimedean solid.

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Truncated order-3 apeirogonal tiling

In geometry, the truncated order-3 apeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t.

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Truncated order-4 apeirogonal tiling

In geometry, the truncated order-4 apeirogonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-4 heptagonal tiling

In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-4 hexagonal tiling

In geometry, the truncated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-4 octagonal tiling

In geometry, the truncated order-4 octagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-4 pentagonal tiling

In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-5 hexagonal tiling

In geometry, the truncated order-5 hexagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-5 pentagonal tiling

In geometry, the truncated order-5 pentagonal tiling is a regular tiling of the hyperbolic plane.

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Truncated order-5 square tiling

In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-6 hexagonal tiling

In geometry, the truncated order-6 hexagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-6 octagonal tiling

In geometry, the truncated order-6 octagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-6 pentagonal tiling

In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-6 square tiling

In geometry, the truncated order-6 square tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-7 heptagonal tiling

In geometry, the truncated order-7 heptagonal tiling is a regular tiling of the hyperbolic plane.

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Truncated order-7 square tiling

In geometry, the truncated order-7 square tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-7 triangular tiling

In geometry, the Order-7 truncated triangular tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane.

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Truncated order-8 hexagonal tiling

In geometry, the truncated order-8 hexagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated order-8 octagonal tiling

In geometry, the truncated order-8 octagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated order-8 triangular tiling

In geometry, the Truncated order-8 triangular tiling is a semiregular tiling of the hyperbolic plane.

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Truncated pentahexagonal tiling

In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated square tiling

In geometry, the truncated square tiling is a semiregular tiling by regular polygons of the Euclidean plane with one square and two octagons on each vertex.

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Truncated tetraapeirogonal tiling

In geometry, the truncated tetrapeirogonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated tetrahedron

In geometry, the truncated tetrahedron is an Archimedean solid.

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Truncated tetraheptagonal tiling

In geometry, the truncated tetraheptagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated tetrahexagonal tiling

In geometry, the truncated tetrahexagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated tetraoctagonal tiling

In geometry, the truncated tetraoctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated tetrapentagonal tiling

In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane.

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Truncated triapeirogonal tiling

In geometry, the truncated triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of tr.

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Truncated triheptagonal tiling

In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane.

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Truncated trihexagonal tiling

In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane.

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Truncated trioctagonal tiling

In geometry, the truncated trioctagonal tiling is a semiregular tiling of the hyperbolic plane.

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Uniform polyhedron

A uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

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Uniform tilings in hyperbolic plane

In hyperbolic geometry, a uniform (regular, quasiregular or semiregular) hyperbolic tiling is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive (transitive on its vertices, isogonal, i.e. there is an isometry mapping any vertex onto any other).

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Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

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Vertex figure

In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.

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3-7 kisrhombille

In geometry, the 3-7 kisrhombille tiling is a semiregular dual tiling of the hyperbolic plane.

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4-5 kisrhombille

In geometry, the 4-5 kisrhombille or order-4 bisected pentagonal tiling is a semiregular dual tiling of the hyperbolic plane.

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Redirects here:

Face configuration, Polyhedron vertex configuration.

References

[1] https://en.wikipedia.org/wiki/Vertex_configuration

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